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Laguerre Series for Asian and Other Options

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  • Daniel Dufresne
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    Abstract

    This paper has four goals: (a) relate ladder height distributions to option values; (b) show how Laguerre expansions may be used in the computation of densities, distribution functions, and option prices; (c) derive some new results on the integral of geometric Brownian motion over a finite interval; and (d) apply the preceding results to the determination of the distribution of the integral of geometric Brownian motion and the computation of Asian option values. The usual fixed-strike options on the average are treated, as well as options with payoffs expressed in terms of one over the average of the underlying security, which this author calls "reciprocal Asian options." In all cases the underlying asset is represented by geometric Brownian motion, the averages are performed continuously, and the options are of European type. Copyright Blackwell Publishers, Inc..

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 10 (2000)
    Issue (Month): 4 ()
    Pages: 407-428

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    Handle: RePEc:bla:mathfi:v:10:y:2000:i:4:p:407-428

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    Cited by:
    1. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," LSE Research Online Documents on Economics 2851, London School of Economics and Political Science, LSE Library.
    3. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    4. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    5. Emmanuel Jurczenko & Bertrand Maillet & Bogdan Negrea, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.

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